The behaviour as \( x\rightarrow 0^{+}, {\rm arg}(x)=0 \)  is quite different, however.
The density has an algebraic divergence here, but it is totally overwhelmed by an exponential suppression.
This is simply illustrated by the large-\(\gamma \)  formula (REF ) and the \( \alpha =1 \)  special cases (REF ).
The asymptotic behaviour of the Fox H-function as \( x\rightarrow 0 \)  with \( {\rm arg}(x)=0 \)  is known,
see [1]} pg. 2 Definition 1.1 and Theorem 1.1, Case 4, Eq. (1.109) in (ii) of Theorem 1.3,
so for \( 0<\gamma <1 \)  and \( \alpha =1 \)  we have
\(h_1(x) \mathop {\sim }\limits _{x \rightarrow 0^{+}} \frac{1}{\gamma \left( \Gamma (1-\gamma ) \right)^{1/\gamma }}x^{-(1-\frac{1}{2}\gamma )/(1-\gamma )}\\ \times \exp \left[ -(1-1/\gamma )\gamma ^{1/(1-\gamma )}\left( \Gamma (1-\gamma ) \right)^{1/(1-\gamma )}x^{-\gamma /(1-\gamma )} \right] .\) 
